Turn set of vertices into a edge
There is no single command that lest you do exactly what you want, but if you select them all in order (individually from left to right or right to left) you can join them with J. The reason there is no single command that allows you to select them all in one go and then fill them is because Blender wouldn't know in which order to join them. It would be like trying to complete a connect the dots with no numbers. Selecting them all in a specific order tells Blender the path to fill.

EDIT: You could also extrude all of the vertices up (or any direction that ensures the resulting edges dont overlap) so that you have a series of vertical edges. Then the Bridge Edge Loops tool (found in the W or CtrlE menus) will fill all the faces in. Then select the extruded vertices with Alt select and delete them leaving just the connected original vertices.